Here are 3 ways to do it:
(Remember you can only count the boxes in the edge once)
Example: The number of squares in the top and at the bottom is 10.
(double it) 10 x 10 = 100
In both sides of the grid, there are 8 squares
(double it) 8 x 8 = 64
Now, you subtract them.
100 - 64 = 36
In this method, we had to count the boxes on each side of the square. The reason why I used 9 because in each side there are 10 boxes but if we don't count the corners twice, we have 9.
For example 9 + 9 + 9 + 9 = 36
In algebra:
n-1 + n-1 + n-1 + n-1 = 36
The second method is adding the two bottom rows and the 2 sides together.
We only count the corners once that's why we have 8 as the side rows.
For example 10 + 10 + 8 + 8 = 36
If we use algebra as a calculation, it will look like this:
n + n + n-2 + n-2 = 36
Do you know any other way to do it?
Hi Faith, i really like your layout and the way you described how you have calculated the number of squares on the outside of a grid. Is there an algebraic formulae for the area method you used in example 1. Perhaps you could have a go at working that out and the show me an example.
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